
Infinite Length Modules
Birkhäuser (Publisher)
Published on 29. October 2012
Book
Paperback/Softback
IX, 439 pages
978-3-0348-9562-0 (ISBN)
Description
This volume presents the invited lectures of a conference devoted to Infinite Length Modules, held at Bielefeld, September 7-11, 1998. Some additional surveys have been included in order to establish a unified picture. The scientific organization of the conference was in the hands of K. Brown (Glasgow), P. M. Cohn (London), I. Reiten (Trondheim) and C. M. Ringel (Bielefeld). The conference was concerned with the role played by modules of infinite length when dealing with problems in the representation theory of algebras. The investi gation of such modules always relies on information concerning modules of finite length, for example simple modules and their possible extensions. But the converse is also true: recent developments in representation theory indicate that a full un derstanding of the category of finite dimensional modules, even over a finite dimen sional algebra, requires consideration of infinite dimensional, thus infinite length, modules. For instance, the important notion of tameness uses one-parameter fami lies of modules, or, alternatively, generic modules and they are of infinite length. If one tries to exhibit a presentation of a module category, it turns out to be essential to take into account the indecomposable modules which are algebraically compact, or, equivalently, pure injective. Specific methods have been developed over the last few years dealing with such special situations as group algebras of finite groups or noetherian rings, and there are surprising relations to topology and geometry. The conference outlined the present state of the art.
More details
Series
Edition
Softcover reprint of the original 1st ed. 2000
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
IX, 439 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 25 mm
Weight
680 gr
ISBN-13
978-3-0348-9562-0 (9783034895620)
DOI
10.1007/978-3-0348-8426-6
Schweitzer Classification
Other editions
Additional editions

Henning Krause | Claus M. Ringel
Infinite Length Modules
Book
08/2000
1st Edition
Springer
€85.55
Article exhausted; check different version
Content
Infinite length modules. Some Examples as Introduction.- Modules with strange decomposition properties.- Failure of the Krull-Schmidt theorem for artinian modules and serial modules.- Artinian modules over a matrix ring.- Some combinatorial principles for solving algebraic problems.- Dimension theory of noetherian rings.- Krull, Gelfand-Kirillov, Filter, Faithful and Schur dimensions.- Cohen-Macaulay modules and approximations.- The generic representation theory of finite fields A survey of basic structures.- On artinian objects in the category of functors between
$${{\mathbb{F}}_{2}}
$$
-vector spaces.- Unstable modules over the Steenrod algebra, functors, and the cohomology of spaces.- Infinite dimensional modules for finite groups.- Bousfield localization for representation theoretists.- The thick subcategory generated by the trivial module.- Birational classification of moduli spaces.- Tame algebras and degenerations of modules.- On some tame and discrete families of modules.- Purity, algebraic compactness, direct sum decompositions, and representation type.- Topological and geometrical aspects of the Ziegler spectrum.- Finite versus infinite dimensional representations A new definition of tameness.- Invariance of tameness under stable equivalence:Krause's theorem.- The Krull-Gabriel dimension of an algebra Open problems and conjectures.- Homological differences between finite and infinite dimensional representations of algebras.